Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays

Arik, Sabri; Tavşanoglu, V.

doi:10.1016/j.neucom.2004.12.002

Cited by 107 publications

(27 citation statements)

References 25 publications

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“…So for, many important results on CNNs have been obtained regarding the existence of equilibria, global asymptotic stability, global exponential stability (Kosto, 1987;1988;Gopalsmy and He, 1994;Cao and Wang, 2002;Cao, 2003;Cao and Dong, 2003;Chen et al, 2004;Liu et al, 2003;Liao and Yu, 1998;Zhao, 2006;2002;Arik and Tavsanoglu, 2005;Tian et al, 2010;Wang et al, 2007;Raja et al, 2011). Especially the investigation of CNNs with periodic coefficients and delays has attracted more and more attention of researchers (Liu and Tang, 2006;Liu and Huang, 2006).…”

Section: Q Zhang Et Almentioning

confidence: 99%

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Zhang¹,

Yang²,

Liao³

2011

International Journal of Applied Mathematics and Computer Science

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Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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Section: Q Zhang Et Almentioning

confidence: 99%

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Zhang¹,

Yang²,

Liao³

2011

International Journal of Applied Mathematics and Computer Science

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“…Many papers have investigated the global stability for continuous-time BAM models with or without time delays [30,31]. In numerical simulations and practical implementation of a continuous-time neural network, discretization is need.…”

Section: Stability Analysis Of Discrete-time Hopfiled Neural Networkmentioning

confidence: 99%

Stability analysis of discrete-time recurrent neural networks based on standard neural network models

Liu

2008

Neural Comput & Applic

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In order to conveniently analyze the stability of various discrete-time recurrent neural networks (RNNs), including bidirectional associative memory, Hopfield, cellular neural network, Cohen-Grossberg neural network, and recurrent multiplayer perceptrons, etc., the novel neural network model, named standard neural network model (SNNM) is advanced to describe this class of discrete-time RNNs. The SNNM is the interconnection of a linear dynamic system and a bounded static nonlinear operator. By combining Lyapunov functional with S-Procedure, some useful criteria of global asymptotic stability for the discrete-time SNNMs are derived, whose conditions are formulated as linear matrix inequalities. Most delayed (or non-delayed) RNNs can be transformed into the SNNMs to be stability analyzed in a unified way. Some application examples of the SNNMs to the stability analysis of the discrete-time RNNs shows that the SNNMs make the stability conditions of the RNNs easily verified.Keywords Standard neural network model (SNNM) Á Global asymptotic stability Á Time-delay system Á Time-varying system Á Discrete-time Á Linear matrix inequality (LMI) Á Hopfield neural network Á Bidirectional associative memory Á Cohen-Grossberg neural network

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“…The circuits diagram and connection pattern implementing for the delayed BAM neural networks can be found in [8]. In recent years, some useful results on the uniqueness and global stability of the equilibrium point for the delayed recurrent neural networks and delayed BAM neural networks have been given, for example, see [1,2,3], [8], [13], [15], [17,18,19] and references therein. It is well known that studies on neural dynamical system not only involve a discussion of stability properties, but also involve many dynamic behavior such as periodic oscillatory behavior, synchronization, dissipativity, bifurcation, and chaos [5,8,9].…”

Section: Introductionmentioning

confidence: 99%

New Conditions on Existence and Global Asymptotic Stability of Periodic Solutions for Bam Neural Networks With Time-Varying Delays

Zhang¹,

Zhou²

2011

Journal of the Korean Mathematical Society

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Abstract. In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

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Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays

Cited by 107 publications

References 25 publications

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Stability analysis of discrete-time recurrent neural networks based on standard neural network models

New Conditions on Existence and Global Asymptotic Stability of Periodic Solutions for Bam Neural Networks With Time-Varying Delays

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